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States32i

Memory32i

Fixtype of memories for the RV32I base.

This is a list of 2^{32} unsigned 8-bit integers, according to stat and stat-validp. Recall that we do not model restrictions on the address space yet.

Definitions and Theorems

Function: memory32i-equiv$inline

(defun memory32i-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (memory32ip acl2::x)
                              (memory32ip acl2::y))))
  (equal (memory32i-fix acl2::x)
         (memory32i-fix acl2::y)))

Theorem: memory32i-equiv-is-an-equivalence

(defthm memory32i-equiv-is-an-equivalence
  (and (booleanp (memory32i-equiv x y))
       (memory32i-equiv x x)
       (implies (memory32i-equiv x y)
                (memory32i-equiv y x))
       (implies (and (memory32i-equiv x y)
                     (memory32i-equiv y z))
                (memory32i-equiv x z)))
  :rule-classes (:equivalence))

Theorem: memory32i-equiv-implies-equal-memory32i-fix-1

(defthm memory32i-equiv-implies-equal-memory32i-fix-1
  (implies (memory32i-equiv acl2::x x-equiv)
           (equal (memory32i-fix acl2::x)
                  (memory32i-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: memory32i-fix-under-memory32i-equiv

(defthm memory32i-fix-under-memory32i-equiv
  (memory32i-equiv (memory32i-fix acl2::x)
                   acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-memory32i-fix-1-forward-to-memory32i-equiv

(defthm equal-of-memory32i-fix-1-forward-to-memory32i-equiv
  (implies (equal (memory32i-fix acl2::x) acl2::y)
           (memory32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-memory32i-fix-2-forward-to-memory32i-equiv

(defthm equal-of-memory32i-fix-2-forward-to-memory32i-equiv
  (implies (equal acl2::x (memory32i-fix acl2::y))
           (memory32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: memory32i-equiv-of-memory32i-fix-1-forward

(defthm memory32i-equiv-of-memory32i-fix-1-forward
  (implies (memory32i-equiv (memory32i-fix acl2::x)
                            acl2::y)
           (memory32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: memory32i-equiv-of-memory32i-fix-2-forward

(defthm memory32i-equiv-of-memory32i-fix-2-forward
  (implies (memory32i-equiv acl2::x (memory32i-fix acl2::y))
           (memory32i-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Subtopics

Memory32ip: Recognizer for memory32i.
Memory32i-fix: Fixer for memory32i.